Ample vector bundles with zero loci of sectional genus two (Q1881529)

Let \(X\) be a smooth and complex projective manifold, \(H\) an ample line bundle on \(X\), \(Z \subset X\) a smooth submanifold, \(E\) an ample vector bundle on \(X\) with rank \(\dim (X)-\dim (Z) \geq 2\) such that \(Z\) is the zero-locus of a section of \(E\). Here the authors classify all these triples with the additional condition that \(H| Z\) is spanned and that the pair \((Z,H| Z)\) is a polarized manifold of sectional genus \(2\): there are \(6\) cases. The authors also put their result in the general program of the classification of ample vector bundles with corank \(1\) and sectional genus \(2\).